A balloon is tied to a peg at (2, -1, 3) by a string of length 5 m…

Step 1. The sphere. The balloon is at distance $5\ \text{m}$ from the peg. So $(x - 2)^2 + (y + 1)^2 + (z - 3)^2 = 25$. The square of the radius is $25\ \text{m}^2$.

Step 2. The distance. $\sqrt{(5 - 2)^2 + (3 + 1)^2 + (3 - 3)^2} = \sqrt{9 + 16} = 5\ \text{m}$.

Step 3. The decision. The distance equals the radius, so the point is on the sphere. The balloon can reach it with the string just taut.